In Proteus Stephen thinks of a recent drowning in Dublin Bay and associates it with his inability to save his dying mother: "A drowning man. His human eyes scream to me out of horror of his death. I... With him together down... I could not save her. Waters: bitter death: lost." Later in the same chapter he anticipates the recovery of the drowned man's body and imagines "the stench of his green grave." In both passages he is recalling a complex of associations that crowded into his mind in Telemachus, linking the green seawater with the death of his mother, and linking his fear of drowning with his fear of being swallowed up in guilt.
Looking out over Dublin Bay from the top of the Sandycove tower in the first chapter, Stephen makes a mental connection to the bowl that sat beside his mother's sickbed: "The ring of bay and skyline held a dull green mass of liquid. A bowl of white china had stood beside her deathbed holding the green sluggish bile which she had torn up from her rotting liver by fits of loud groaning vomiting." He thinks of the connection again after Mulligan goes down to the living quarters, and he sees a cloud "shadowing the bay in deeper green. It lay behind him, a bowl of bitter waters."
Mulligan has probably helped to shape Stephen's associative connections, with his comment about "The snotgreen sea," and his suggestion that it should be called "a great sweet mother," or "Our mighty mother!" Yeats has reinforced the bitterness of the green bile, by singing of “love’s bitter mystery”—a song that makes Stephen think of his mother. The memory of the "square ditch" at Clongowes, with its unhealthy green "scum," has no doubt played its part as well.